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(D) According to the Stefan-Boltzmann law,the radiant energy emitted by a black body is proportional to the fourth power of its absolute temperature,i

Vedclass · Accepted Answer

$320$

Vedclass · Answer

(D) According to the Stefan-Boltzmann law,the radiant energy emitted by a black body is proportional to the fourth power of its absolute temperature,i.e.,$E \propto T^4$.Let $E_1$ be the initial radiant energy and $T_1$ be the initial temperature of the sun. Let $E_2$ be the new radiant energy and $T_2$ be the new temperature.Given: $E_1 = 20 \ kcal/m^2-min$ and $T_2 = 2T_1$.Using the ratio formula:$\frac{E_2}{E_1} = \left(\frac{T_2}{T_1}ight)^4$Substituting the values:$\frac{E_2}{20} = \left(\frac{2T_1}{T_1}ight)^4$$\frac{E_2}{20} = (2)^4$$\frac{E_2}{20} = 16$$E_2 = 16 	imes 20 = 320 \ kcal/m^2-min$.

The radiant energy from the sun incident normally at the surface of the earth is $20 \ kcal/m^2-min$. What would have been the radiant energy incident normally on the earth if the sun had a temperature twice of the present one? (in $kcal/m^2-min$)

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